Last visit was: 13 Jul 2025, 06:19 It is currently 13 Jul 2025, 06:19
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Jul 2025
Posts: 102,638
Own Kudos:
Given Kudos: 98,177
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,638
Kudos: 740,957
 [82]
4
Kudos
Add Kudos
78
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Jul 2025
Posts: 102,638
Own Kudos:
Given Kudos: 98,177
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,638
Kudos: 740,957
 [10]
4
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
General Discussion
User avatar
Ankur9
Joined: 25 May 2014
Last visit: 11 May 2016
Posts: 43
Own Kudos:
50
 [1]
Given Kudos: 125
Products:
Posts: 43
Kudos: 50
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
Naina1
Joined: 05 Feb 2015
Last visit: 05 Jun 2016
Posts: 39
Own Kudos:
Given Kudos: 8
Concentration: Finance, Entrepreneurship
WE:Information Technology (Healthcare/Pharmaceuticals)
Posts: 39
Kudos: 82
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think it would be C.
Both statements together gives R>3
1 only does not give any information. Consider M, N and P to be 2, 4, 6 respectively. It doesn't tell anything about the value of R.

2 only is also insufficent. If R=3 and M=6 N=7 P=8
It gives S=2
Also, if M=6 N=4 P=2, then for S to be 2 R has to be greater than 3.

1+2) No combination of M, N and P as positive even integers gives the sum >=20. So, in order for S=2 the extra value should come from the sum of R+R+R i.e. 3R and for that R has to be greater than 3.
avatar
fhp
Joined: 16 Mar 2015
Last visit: 11 Apr 2016
Posts: 2
Own Kudos:
Given Kudos: 1
Posts: 2
Kudos: 10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Pretty sure it's D.

With statement 1, adding together any combination of three digits between 2,4,6, and 8 gives you a two digit number with the second digit being one of the already used digits from 2,4,6, and 8. For instance, 2+4+6=12. 4+6+8=18, etc. This means that the ones column, or the Rs, need to add up to be at least 10 so you can carry a 1 and avoid the redundancy between number "T" and numbers "M","N", and "P." In order to achieve that, the "R"s have to be more than 3, since 3+3+3 is 9. Therefore Statement 1 is sufficient.

With statement 2, we know that "M","N" and "P" have to add up to at least 18 (since the most we could carry over from the "R"s in the addition process would be a 2). This means that "M","N" and "P" have to either be 7-6-5, 8-7-6, or 9-8-7.
7+6+5=18, so R would have to be 7 or 9, to get 21 or 27, but both of these involve repeating numbers so they won't work.
8+7+6=21, so R can be any of the remaining numbers, but 3 is the only one that works without any redundancies.
9+8+7=24, so R can be any of the remaining numbers, but again, 1 is the only one that works without any redundancies.
Neither of those possibilities are greater than 3, so statement 2 is also sufficient.
User avatar
peachfuzz
Joined: 28 Feb 2014
Last visit: 27 Jan 2018
Posts: 269
Own Kudos:
349
 [4]
Given Kudos: 132
Location: United States
Concentration: Strategy, General Management
Products:
Posts: 269
Kudos: 349
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
[quote="Bunuel"]

M, N, R, S, T and V are distinct digits.

R > 3?

(1) M, N and P are positive even integers
M, N, P could be 2, 4, 6, or 4, 6, 8 or 2, 6, 8
If the digits of M, N, P is 2, 4, 6, then S and T would be 1 and 2. This is not possible because M is 2 and T is 2 and that goes against the "distinct integers"
In fact, 4,6,8 and 2,6,8 all result in a repeated digit for T.
R then must be relatively larger. in this case at least 4 in order to change the value of T to a digit that is distinct.
Sufficient

(2) S = 2
96+46+76=218
R>3? yes
90+80+70=240
R>3? no
insufficient

Answer: A
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 11 Jul 2025
Posts: 16,101
Own Kudos:
74,300
 [1]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,300
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fhp
Pretty sure it's D.

With statement 1, adding together any combination of three digits between 2,4,6, and 8 gives you a two digit number with the second digit being one of the already used digits from 2,4,6, and 8. For instance, 2+4+6=12. 4+6+8=18, etc. This means that the ones column, or the Rs, need to add up to be at least 10 so you can carry a 1 and avoid the redundancy between number "T" and numbers "M","N", and "P." In order to achieve that, the "R"s have to be more than 3, since 3+3+3 is 9. Therefore Statement 1 is sufficient.

With statement 2, we know that "M","N" and "P" have to add up to at least 18 (since the most we could carry over from the "R"s in the addition process would be a 2). This means that "M","N" and "P" have to either be 7-6-5, 8-7-6, or 9-8-7.
7+6+5=18, so R would have to be 7 or 9, to get 21 or 27, but both of these involve repeating numbers so they won't work.
8+7+6=21, so R can be any of the remaining numbers, but 3 is the only one that works without any redundancies.
9+8+7=24, so R can be any of the remaining numbers, but again, 1 is the only one that works without any redundancies.
Neither of those possibilities are greater than 3, so statement 2 is also sufficient.

A quick tip - The two statements cannot give you contradictory answers. They are a part of the same puzzle. If the question is "what is x?" Stmnt 1 cannot give you x = 4 if stmnt 2 gives you x = 5. If you get contradictory answers, it means you have messed up somewhere. Here, apparently, stmnt 1 gives you that R is greater than 3 while stmnt 2 gives you that R cannot be greater than 3 - these contradict. So you must have messed up in one of the statements. Go back to see which one.

Interestingly, four solutions above give four different answers!
User avatar
yenh
Joined: 16 Mar 2014
Last visit: 19 Sep 2020
Posts: 15
Own Kudos:
Given Kudos: 123
GMAT Date: 08-18-2015
Products:
Posts: 15
Kudos: 57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Correct answer is D.
Here is my explanation:
(1) M, N, P are even integers and cannot be 0 => M, N, P can be any of the set A {2, 4, 6, 8}. In any case M + N + P > 10.
_ Assumption: R < or = 3 => 3R < 10 -> there is no 1 carried to the tenth -> M + N + P is even (sum of 3 even integers is an even integer). So far we know that M, N, P, T are 4 different even integers and cannot be 0 (sum of any 3 even integers in set A above is > 10).
_ Note that sum M + N + P always contains 10 (2+8 or 4+6) -> the unit digit of sum M + N + P will be M/N/P but not T -> contrast to the question stem.
=> Assumption is wrong => R > 3 : Sufficient.

(2) S = 2 => M + N + P + (3R / 10) >= 20. Because Max(M + N + P) = 4 + 6 + 8=18 => 3R > 20 => R > 3 : Sufficient.

Answer: D
Hope you guys can understand my answer :(
avatar
Udai
Joined: 05 Mar 2013
Last visit: 03 Jan 2017
Posts: 37
Own Kudos:
Given Kudos: 12
Location: United States
GMAT 1: 670 Q49 V33
GPA: 3.56
WE:Marketing (Telecommunications)
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Its E because even f we combine both the statements we will be able to get both R>3 and R< 3
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,488
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,488
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

Can you confirm that the question is written correctly:

Is "P" supposed to be included in the list of distinct digits or can it be a DUPLICATE of one of them?

GMAT assassins aren't born, they're made,
Rich
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 11 Jul 2025
Posts: 16,101
Own Kudos:
74,300
 [1]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,101
Kudos: 74,300
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
Hi Bunuel,

Can you confirm that the question is written correctly:

Is "P" supposed to be included in the list of distinct digits or can it be a DUPLICATE of one of them?

GMAT assassins aren't born, they're made,
Rich

P is also supposed to be in the list of distinct digits - all digits are distinct. I missed it in the original question.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Jul 2025
Posts: 102,638
Own Kudos:
Given Kudos: 98,177
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,638
Kudos: 740,957
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
EMPOWERgmatRichC
Hi Bunuel,

Can you confirm that the question is written correctly:

Is "P" supposed to be included in the list of distinct digits or can it be a DUPLICATE of one of them?

GMAT assassins aren't born, they're made,
Rich

P is also supposed to be in the list of distinct digits - all digits are distinct. I missed it in the original question.

Edited. Thank you both!
User avatar
verysecretive3
Joined: 23 Mar 2018
Last visit: 27 Mar 2024
Posts: 55
Own Kudos:
Given Kudos: 11
Location: India
GMAT 1: 750 Q48 V44
GPA: 3.6
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's start by analysing the first statement
It is given that M,N and R are positive even integers. We have 4 options for this: 2,4,6,8 The sum of any three of them will give a repeat digit. For eg: 2+4+6= 12 (t=2) This is not possible as M and T must be distinct
4+6+8= 18 (t=8) This is not possible as M and T must be distinct
For T to be different from M,N and R, it must be odd. This will happen if we have a carry-over from R+R+R=3R
3R>10 for the carry-over hence R>3. Sufficient.

(2) S=2
This is not sufficient because we get S=2 with values of R greater than 3 and less than 3.
User avatar
amit9424444
Joined: 22 Feb 2020
Last visit: 28 Apr 2025
Posts: 4
Given Kudos: 31
Posts: 4
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think It' C ,

Statement 1 :- M. N, P positive even integers by this statement we just know the result is a 3 digit number
Even numbers :- Lets see both possibilities
1 :- 82+62+42 =186 this shows r<3
2 :- 89+69+49 = 207 this shows r>3

Statement 2 :- S= 2 (We are here just taking st 2 in consideration only)
1 :- 89+79+69 = 227 R>3
2 :- 82+72+62 = 216 R<3 Both are possibilities

Taking both statement in consideration :- We know s=2 and even numbers taken into consideration.
there are 3 numbers which can be formed 204,207,201 where R has to be greater than 3

Hence it should be C
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Jul 2025
Posts: 102,638
Own Kudos:
740,957
 [1]
Given Kudos: 98,177
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,638
Kudos: 740,957
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
amit9424444
I think It' C ,

Statement 1 :- M. N, P positive even integers by this statement we just know the result is a 3 digit number
Even numbers :- Lets see both possibilities
1 :- 82+62+42 =186 this shows r<3
2 :- 89+69+49 = 207 this shows r>3

Statement 2 :- S= 2 (We are here just taking st 2 in consideration only)
1 :- 89+79+69 = 227 R>3
2 :- 82+72+62 = 216 R<3 Both are possibilities

Taking both statement in consideration :- We know s=2 and even numbers taken into consideration.
there are 3 numbers which can be formed 204,207,201 where R has to be greater than 3

Hence it should be C

You can check the correct answer under the spoiler in the original post.

The stem specifies that "M, N, P, R, S, T and V are distinct digits". Do your examples satisfy this condition?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,375
Own Kudos:
Posts: 37,375
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Math Expert
102638 posts